From ek and zeteo; to search out, i.e. (figuratively)investigate, crave, demand, (by Hebraism) worship -- en- (re-)quire, seek after (carefully, diligently).
see GREEK ek
see GREEK zeteo
a. to seek out, search for: properly, τινα, 1 Macc. 9:26; figuratively: τόν κύριον, τόν Θεόν, to seek the favor of God, worship him, Acts 15:17; Romans 3:11 (Tr marginal reading WH marginal reading ζητῶν); Hebrews 11:6 (Psalm 13:2 b. to seek out i. e. investigate, scrutinize: τί, Sir. 39:1, 3; περί τίνος, to examine into anything, 1 Peter 1:10, where it is joined with ἐξερευναν (to seek out and search out), as in 1 Macc. 9:26. c. to seek out for oneself, beg, crave: Hebrews 12:17. d. to demand back, require: τό αἷμα τῶν προφητῶν ἀπό τῆς γενεάς ταύτης, to take vengeance on this generation for the slaughter of the prophets (after the Hebrew, cf. 2 Samuel 4:11; Ezekiel 3:18; see ἐκ, I. 7): Luke 11:50 (51). (In secular authors thus far only a single passage has been noted in which this word appears, Aristid. or. 8, i., p. 488 (i. e. orat. 38, i., p. 726, Dindorf edition).)